Peak to average power ratio reduction in communication systems

ABSTRACT

A system and method for reducing peak to average power ratio (PAR) in single and multi-carrier transmitters while accounting for the effect of the transmit filters without significantly affecting a requisite transmission Power Spectral Density (PSD) mask. To this end, in a multicarrier communication system, a DSL transmitter is provided that transmits a multicarrier symbol having a controlled peak-to-average power ratio (PAR) and which is a function of a plurality of information signals. The transmitter has a power reducer that reduces the PAR of the multicarrier symbol by modifying a selected information signal of a plurality of information signals, the modified signal including an information component, a peak reduction component, and a transmission channel response component.

BACKGROUND OF THE INVENTION

[0001] The present invention relates generally to single carrier andmulti-carrier communication systems, and particularly to reducing Peakto Average power Ratios (“PAR”) in such systems.

[0002] Multi-carrier transmission systems have evolved out of a need toprovide increased transmission rates for information via existingcommunication channels. In its broadest aspect, multi-carrier systemstransmit a number of independent signals on a common channel. Eachmodulated signal is centered on a different frequency, the frequenciesbeing normally equally spaced within a predetermined transmissionbandwidth of the channel. These frequencies are commonly termed carrierfrequencies.

[0003] Transmission channels are fundamentally analog and thus mayexhibit a variety of transmission effects. In particular, telephonelines, as for example Digital Subscriber Line (DSL) Systems (DSLs) usesome form of modulation.

[0004] A transmitter system normally converts each successive group of bbits from a digital bit stream into one of 2^(b) data symbols x_(m) viaa mapping (generally one-to-one) using an encoder. Each group of b bitsconstitutes a message m, with M=2^(b) possible values. The data symbolsare N-dimensional vectors x_(m) and the set of M vectors form a signalconstellation. Modulation is the process of converting each successivedata symbol vector into a continuous-time analog signal x_(m)(t) thatrepresents the message corresponding to each successive group of b bits.

[0005] A particular implementation of a multi-carrier system is aDiscrete Multi-Tone (DMT) scheme that partitions the availabletransmission bandwidth into many narrow-band subchannels over whichparallel data streams are modulated. The DMT technique has been adoptedfor use in Asymmetric Digital Subscriber Line (ADSL) technology. InADSL, DMT is used to generate 224 separate subchannels (that is “tones”)that are 4.3125 kHz wide and that are located between 138 kHz to 1.104MHz for downstream transmission to an end user, and 26 separatesubchannels that are located between 26 kHz to 138 kHz for upstreamtransmission from the end user.

[0006]FIG. 1 illustrates a typical DMT transmitter 10. The transmitterincorporates several components including an encoder 102 and a discretemulti-tone modulator 104. The encoder 102 segments the incoming bitstreams and encodes it such that it can be transmitted over severaldifferent carriers N. The encoder 102 outputs data sequences for the Nchannels. Modulator 104 modulates the segmented data inputs using anappropriate modulation scheme such as QAM. These inputs are complexinputs that are passed to a discrete multi-tone modulator. The output ofthe modulator 104 provides the DMT vector of constellation points Xcomprised of the individual channel subsymbols. An Inverse FourierTransformer (IFFT) 106 transforms X to provide a discrete timeequivalent by any suitable algorithm. The IFFT 106 is used forconverting the frequency domain vector X to the time domain vector x.After the encoded signal has been modulated to form a discretemulti-tone signal, a cyclic prefix is appended 108 to the discretemulti-tone encoded signal. The cyclic prefix is used primarily tosimplify the demodulation of the discrete multi-tone signals. The cyclicprefix is a replica of the last several samples of the digital signaland is required for DMT transmissions to mitigate inter-symbolinterference. The transmitter 10 also includes a series of digitalfilters 110, Digital to Analog Converter (DAC) 112, analog filters 114and a line driver 116.

[0007] The discrete time signal is passed through the digital filter 110before being processed by the DAC 112. The DAC 112 converts the discretetime signal into a continuous time signal. The continuous time signal isapplied via the analog filters 114, to the line driver 116. The linedriver 116 drives the signal onto the communication line 118, which maytake the form of a twisted pair phone line. The discrete multi-toneencoded signal with its cyclic prefix is then transmitted over thecommunication line to a remote location (not shown).

[0008] The transmission capability of the individual channels isevaluated for each connection, and data is allocated to the subchannelsaccording to their transmission capabilities (the number of bits eachchannel can support). The bit distribution is determined adaptively indiscrete multi-tone systems. To facilitate this, the transmitter alsoincludes a line monitor (not shown) that monitors the communication lineto determine the line quality of each of the available subchannels. Thedetermination of what subchannels to transmit the encoded data over aswell as how much data to transmit over each subchannel is dynamicallydetermined on the basis of several factors. The factors include thedetected line quality parameters, subchannel gain parameters, apermissible power mask, and the desired maximum subcarrier bit-errorrates. Subchannels that are not capable of supporting data transmissionare not used, whereas the bit-carrying capacity of subchannels that cansupport transmission is maximized. Thus, by using DMT in an ADSL system,the transmission capability of each twisted pair connection ismaximized.

[0009] As mentioned with reference to FIG. 1, summing the modulatedcarriers creates a DMT symbol. Summing many random modulated carriersleads to a transmitted signal whose power probability density functionis very close to Gaussian. In other words if viewed in the time domainas one-dimensional signals, the probability distribution of multichannelsignals approaches a Gaussian distribution. Thus the DMT symbol has amuch higher Peak-to-Average power Ratio (PAR) than most single carriersignals. A clip is defined to occur when the transmit signal sampleexceeds the maximum implemented value for the transmitter (often set bythe DACs maximum value) or a predetermined threshold. For example, for aclipping probability of 10-7, the PAR of a Gaussian signal isapproximately 5.33 (or 14.5 dB) as opposed to 2.45 (or 7.8 dB) for asingle carrier. Therefore, in order to minimize clipping of the DMTsignal, DMT systems must use a Digital to Analog Converter (DAC) withhigh resolution and an Analog Front End (AFE) with a large dynamicrange. Since the AFE can constitute a significant percentage of the costof the system as well as the power drainage of the system, it isdesirable to reduce the PAR of the signal at these components forreducing their requirements and saving power.

[0010] Many PAR reduction methods have been proposed as exemplified inU.S. Pat. No. 5,623,513, U.S. Pat. No. 5,787,113, U.S. Pat. No.5,768,318, U.S. Pat. No. 5,835,536, and in a document by J. Tellado, J.Cioffi, entitled “Further Results on Peak-to-Average Ratio Reduction”,ANSI contribution T1E1.4/98-252, August 1998. The methods disclosedtherein modify the DMT transmitter in such way that the PAR of thesignal immediately output from the modulator 104 is reduced. PARreduction ranging between 2 and 6 dB from the 14.5 dB figure has beenachieved in these systems.

[0011] Another method of achieving PAR reduction is described in “PARReduction in Multicarrier Transmission Systems”, ANSI contributionT1E1.4/97-367, December 1997 and in PCT Application No. PCT/US99/08682.This method consists of adding a waveform, or peak reducing kernels, tothe DMT symbol such that the peak of the kernel cancels the peaks of thesignal. In FIG. 3, a block diagram of an implementation of the peakreducing kernel method is illustrated generally by the numeral 30.Selection of the peak reduction frequencies is made in advance.Generally those frequencies in the channel that have a lot of noise andare capable of only carrying low bit rate signals are used as peakreduction frequencies. The particular kernel is also computed beforehandbased upon the selection of the peak reduction frequencies. A scaled andcyclically shifted replica of the kernel is added to the output of themodulated signal, x(n), to cancel its largest peak. This procedure isrepeated for the next largest peak and continues for a fixed number ofiterations or until all the peaks larger than a given threshold has beenreduced. Therefore, the final waveform of the kernel added to the signalx(n) is of the form:$\sum\limits_{i}{A_{i}{k\left( {n - n_{i}} \right)}_{{modulo}\quad N}}$

[0012] where A_(i) is the amplitude of the ith element, n_(i) is thephase shift of the ith element, and N is the DMT symbol size. Thus thescaled and delayed kernel is added to x resulting in x^(clip)=x+k, wherek is a linear combination of one ore more kernels that that have beenscaled and time delayed to negate one or more peaks in x.

[0013] Since the kernel is not necessarily zero outside of its peak, asignal peak that has been reduced below a threshold may rise above thethreshold while reducing other signal peaks. Therefore, the kernel,k(n), is chosen to be impulse-like for minimizing the probability ofregenerating peaks.

[0014] Furthermore, in order not to interfere with the datatransmission, the kernel is chosen such that in the frequency domain, itis orthogonal to the data carriers and satisfies the property:

X _(k) ·K _(k)=0

[0015] where X_(k) is signal in the frequency domain and K_(k) is thekernel in the frequency domain. In other words, the kernel is zero indata carrying carriers and no data is transported in carriers reservedfor the kernel. FIGS. 2(a) and (b) show the relationship between X and Kin the frequency domain. In practice, only a small percentage of theavailable carriers need to be reserved for the kernel, thereby causingonly a small reduction in data rate.

[0016] Although the above techniques are successful in reducing the PAR,it has been recognized by J. Tellado and J. Cioffi, in ANSI contributionT1E1.4/98-252, August 1998 entitled “Further Results on Peak-to-AverageRatio Reduction,” that the digital filters 110 and analog filters 114regenerate the PAR that was reduced at the output of the IFFT 106 andleads to negligible benefits at the DAC 112 or line driver 116. Sincethe transmit filters (digital 110 and/or analog 114) are essential formeeting the transmission Power Spectral Density (PSD) mask, they cannotbe eliminated to avoid PAR losses.

[0017] Referring to FIG. 3, there is a block diagram of a transmitterincluding a PAR reducer. This transmitter uses peak reducing kernelsaccording to a known technique. The transmitter 30 includes a encoder102 and modulator 104, an IFFT 106, a PAR reducer 302, cyclic prefixinsertion module 108, digital filters 110, DAC 112, analog filters 114and line drivers 116. Modulator 104 provides a frequency domain signal Xto the IFFT 106. The IFFT 106 applies an inverse Fourier transform to Xto produce a discrete time signal x(n). In the case of DMT a discretetime signal x is generated from a number of complex valued QAM modulatedsignals, which are the components of X. Each element of x(n) is a symbolderived from X defined by:${{x(n)} = {\frac{1}{\sqrt{N}}{\sum\limits_{k = 0}^{N - 1}{X_{k}^{j\quad 2\quad \pi \quad {{kn}/N}}}}}},{k = 0},{{\ldots \quad N} - 1}$

[0018] which can be written as x=QX where Q is the IFFT matrix and theelements of Q are$q_{n,k} = {\frac{1}{\sqrt{N}}^{{j2}\quad \pi \quad {{kn}/N}}}$

[0019] where:

[0020] N is the number of channels or tones;

[0021] X is the DMT vector of constellation points mapped from the m-thblock of encoded bits;

[0022] x is the time vector transformed from X by the IFFT; and

[0023] n is a discrete time indexing and denotes Nyquist Rate samples.

[0024] The PAR reducer 302 performs a PAR reduction on x(n) by applyingpeak reducing kernels to x(n). More specifically, the PAR reducer 302adds peak reduction signals k to x(n) in order to reduce the PAR ofx(n). Selection of the peak reduction frequencies is made in advance.Generally those frequencies in the channel that have a great deal ofnoise and are capable of only carrying low bit rate signals are used aspeak reduction frequencies. The particular kernel may also be computedbeforehand based upon the selection of the peak reduction frequencies.It is assumed that the receiver is informed of which frequencies arepeak reduction frequencies. This information may be transmitted to thereceiver just before a new set of peak reduction frequencies is used.

[0025] The values of the peak reduction signals may be represented as avector c in the time domain and the vector C in the frequency domain.Thus

[0026] x+c=Q(X+C) and the possible values of c are chosen to reduce thePAR in the signal x. The time domain signal generated by the vector x+cis then the desired PAR reduced signal.

[0027] As mentioned above, the peaks in the time domain signal x(t) canbe scaled by adding or subtracting an appropriately scaled impulsefunction at those peak time values. The impulse function is normallyconstructed from the selected peak reduction frequencies and can be usedto create the approximate impulse function k(t) or kernel. Since K hasnon-zero values only at the peak reduction frequencies, C may berepresented as a linear combination of K. The linear combinations of Kcorrespond to the scaled and shifted versions of the kernel k such thatscaled and shifted versions of k negate the peaks of x.

[0028] A scaled and cyclically shifted replica of the kernel is added tothe output of the modulated signal x(n) to cancel its largest peak. Ifonly one peak is minimized during a single iteration of applying thekernel k then y=x+A_(i)k(n−n_(i))_(modN) in the discrete time domain,where A is a scaling factor and n, is a time shift. This procedure isrepeated for the next largest peak and continues for a fixed number ofiterations or until all the peaks larger than a given threshold havebeen reduced. Therefore, the final waveform of the kernel added to thesignal x(n) is of the form:$\sum\limits_{i}{A_{i}{k\left( {n - n_{i}} \right)}_{{mod}\quad N}}$

[0029] where Ai is the amplitude of the jth element, n_(i) is the phaseshift of the ith element, and N is the DMT symbol size. Once the PARreducer 302 has finished reducing the peak to average power ratio of thesignal x, it provides x as another symbol of the discrete time sequencey(n) to the cyclic prefix block 108 where${y(n)} = {{x(n)} + {\sum\limits_{i}{A_{i}{{k\left( {n - n_{i}} \right)}_{{mod}\quad N}.}}}}$

[0030] The sequence y(n) is filtered by digital filter 110, to produce asequence w(n)=y(n)⊕h(n) where ⊕ denotes convolution and h(n) is theresponse of the digital filter, before being passed through to DAC 112and the filter 114 to get the continuous time signal for transmission.(A detailed description of this process is described in PCT ApplicationNo. PCT/US99/08682.)

[0031] The above scheme does not take into consideration the effect ofthe filters 110 and 114 in reducing the PAR. Accordingly, there isneeded a PAR reduction mechanism capable of addressing the effect of thedigital and analog filters to reduce the PAR after filtering at variouspoints in the transmitter.

SUMMARY OF THE INVENTION

[0032] According to the invention, a system and method are provided forreducing peak to average power ratio (PAR) in single and multi-carriertransmitters while accounting for the effect of the transmit filterswithout significantly affecting a requisite transmission Power SpectralDensity (PSD) mask. To this end, in a multicarrier communication system,a DSL transmitter is provided that transmits a multicarrier symbolhaving a controlled peak-to-average power ratio (PAR) and which is afunction of a plurality of information signals. The transmitter has apower reducer that reduces the PAR of the multicarrier symbol bymodifying a selected information signal of a plurality of informationsignals, the modified signal including an information component, a peakreduction component, and a transmission channel response component.

[0033] In accordance with a further aspect of the invention, a method isprovided for reducing the peak-to-average ratio (PAR) of a multicarriercommunication system, employing a multicarrier symbol as a function of aplurality of signals, each of the plurality of signals centered at eachone of a plurality of frequencies, the method comprising:

[0034] (a) analyzing the multicarrier symbol to detect a peak in themulticarrier symbol;

[0035] (b) determining a first signal of the plurality of signals thatcontributes to the peak; and

[0036] (c) modifying the first signal by applying a peak reductioncomponent to the first signal, the peak reduction component including atransmission channel component whereby by the PAR of the multicarriersymbol is reduced to compensate for the transmission channel effects onthe power of the symbol.

[0037] The invention will be better understood upon reference to thefollowing detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Embodiments of the invention will now be described by way ofexample only, with reference to the accompanying drawings in which:

[0039]FIG. 1 is a block diagram of a Discrete Multi Tone (DMT)transmitter;

[0040] FIGS. 2(a) and (b) illustrate a frequency domain representationof X and K;

[0041]FIG. 3 is a block diagram of a transmitter having PAR reductionusing peak reducing kernels according to the prior art;

[0042]FIG. 4 is a block diagram of a transmitter having PAR reduction inaccordance with an embodiment of the present invention; and

[0043]FIG. 5 is a block diagram of a transmitter having PAR reduction inaccordance with a further embodiment of the present invention.

DESCRIPTION OF THE SPECIFIC EMBODIMENTS

[0044] In the following description, like numeral refer to likestructures in all of the drawings. Referring to FIG. 4, there is shown atransmitter 40 according to one embodiment of the present invention. Thetransmitter 40 includes a encoder 102 and modulator 104 as describedpreviously, an IFFTs 106, 410, 412, a PAR reducer 302, cyclic prefixinsertion module 108, digital filters 110, DAC 112, analog filters 114and line drivers 116. The cyclic prefix insertion module 108, digitalfilters 110, DAC 112, analog filters 114 and line drivers 116 aredescribed previously and shown as block 118 in FIG. 1.

[0045] The PAR reduction in this embodiment is implemented as follows.The modulator 104 outputs the frequency domain DMT symbols X. The symbolX is combined 404 with a complex weighting vector W representing thefrequency and phase response for the transmit filters 110 and 114 foreach channel. The resulting signal is transformed by an IFFT 406 to{overscore (x)}(n). Similarly, peak reduction kernel K (as describedwith reference to FIG. 3) are combined 408 with the complex weightingvector W. The resulting weighted peak reduction signal is transformed byan IFFT 410 to {overscore (k)}(n) . The PAR reducer 302 receives the{overscore (x)}(n) and {overscore (k)}(n). PAR reduction is performed onthe weighted DMT symbol {overscore (x)}(n), using a similarly weightedversion of the kernel {overscore (k)}(n) to produce:$\overset{\_}{y(n)} = {\overset{\_}{x(n)} + {\sum\limits_{i}{{\overset{\_}{A}}_{i}{\overset{\_}{k}\left( {n - {\overset{\_}{n}}_{i}} \right)}_{{mod}\quad N}}}}$

[0046] The amplitudes {overscore (A)}_(i) and shifts {overscore (n)}_(i)of the weighted kernel {overscore (k)}(n) are stored in memory.Therefore, the weighted DMT symbol {overscore (x)}(n) is a model of thefiltered non-weighted DMT symbol x(n), which is the DMT symbol to betransmitted. The stored amplitudes {overscore (A)}_(i) and shifts{overscore (n)}_(i) of the weighted kernel {overscore (k)}(n) areapplied to the non-weighted kernel k(n), which is added to thenon-weighted DMT symbol x(n). The result${y(n)} = {{x(n)} + {\sum\limits_{i}{{\overset{\_}{A}}_{i}{k\left( {n - {\overset{\_}{n}}_{i}} \right)}_{{mod}\quad N}}}}$

[0047] is a signal that will have a reduced PAR that includes theeffects of the transmit filters.

[0048] More specifically, if the weighting vector W_(k) includes onlythe digital filters, then PAR reduction occurs after the digitalfilters. On the other hand if W_(k) includes the response of the digital110 and analog 114 filters, then PAR reduction occurs after the analogfilters (i.e. immediately preceding the line driver).

[0049] This method may cause an error due to the effective circulartime-domain convolution, which is inherent to frequency-domain weighting(the dot-product of two frequency-domain sequences W_(k) and X_(k)corresponds to the circular convolution of their respective time seriesequivalents, w₁ and x₁ (where {w_(i)}=IFFT({W_(k)}) and{x_(i)}=IFFT({X_(k)})). This error will be small since the impulseresponse of the filters contains most of its energy in a fraction of aDMT symbol.

[0050] In another embodiment of the invention, the effect of the filterson the PAR may be compensated for in the time domain. As shown in FIG.5, the PAR reduction can occur after the digital filters 1 10. Onceagain a transmitter 50 includes the encoder 102 and modulator 104 asdescribed previously, the IFFT 106, a PAR reducer 302, a cyclic prefixinsertion module 108, digital filters 110, DAC 112, analog filters 114and line drivers 116. In this case, however, the kernel needs to beextended by the cyclic prefix and filtered as if it had been injected atpoint A. With this method, instead of having$\sum\limits_{i}{A_{i}{k\left( {n - n_{i}} \right)}}$

[0051] as the injected kernels at point B, we have$\sum\limits_{i}{A_{i}{k_{i}(n)}}$

[0052] as the injected kernels at point C, where

k _(i)(n)=[k(n−n _(i))]_(+CP) εh(n)

[0053] where

[0054] +CP represents the cyclic prefix insertion,

[0055] ε represents linear convolutions and

[0056] h(n) represents the impulse response of the transmit filters.

[0057] Since the kernel is shifted after a prefix has been added and ithas passed through the filters 110 and 112, the shift is no longercircular. The loss of shifting circularity does, however, complicate thePAR reduction process. The increase in complexity requires eitherpre-computing or storing the shifted kernels or re-computing the shiftedkernels each time it is required. Storing the kernels comes at theexpense of extra memory, whereas re-computing the kernels comes at theexpense of more processing power.

[0058] Furthermore, the loss of shifting circularity causes the kernelsadded for symbol i to extend into symbol (i+1). Hence PAR reduction isoperating on the sum of the tail of those kernels and the next symbol.Therefore, the tail of the kernel, or that part of the kernel whichextends into symbol (i+1), must be included in sum of the next symbolprior to determination of the A_(i+1) and k_(i+1) for this ‘i+1’thsymbol.

[0059] The detailed description of specific embodiments above refers topower reduction as it relates to transmitters. However, power reductionof the present invention may also be applied to a receiver for reducingits dynamic range and resolution requirements of the AFE andanalog-to-digital converter at the receiver. In particular, thetransmission channel from the transmitter to the receiver could bemodeled as a filter. PAR is then performed by weighting the peakreduction kernels in a manner as described earlier. Alternatively, powerreduction could be performed on a signal using kernels which have beenalready compensated for the filter effects of the transmission channel.

[0060] Furthermore, although the invention has been described withreference to a DMT communication system, the invention may be applied toany type of communication system including orthogonal frequency divisionmultiplexing (OFDM), discrete wave multitone (DWT), vector codingmodulation, or any single-carrier or multicarrier communication system.

[0061] Although the invention has been described with reference tocertain specific embodiments, various modifications thereof will beapparent to those skilled in the art without departing from the spiritand scope of the invention as outlined in the claims appended hereto.

What is claimed is:
 1. A transmitter for use in a multicarriercommunication system, the transmitter for transmitting a multicarriersymbol, the multicarrier symbol having a peak-to-average power ratio(PAR) and being a function of a plurality of information signals, thetransmitter comprising: (a) a power reducer, wherein the power reduceris operative to reduce the PAR of the multicarrier symbol by modifying aselected information signal of the plurality of information signalswherein the modified signal includes an information component, a peakreduction component, and a transmission channel response component. 2.The transmitter according to claim 1 wherein said power reducercomprises: means for analyzing the multicarrier symbol to detect a peakin the multicarrier symbol; means for determining a first signal of theplurality of signals that contributes to the peak; and means formodifying the first signal by applying a peak reduction component to thefirst signal, the peak reduction component including a transmissionchannel component such that by the PAR of the multicarrier symbol isreduced to compensate for the transmission channel effects on the powerof the symbol.
 3. A method for reducing the peak-to-average ratio (PAR)of a multicarrier communication system, wherein the multicarrier symbolis a function of a plurality of signals, each of the plurality ofsignals centered at each one of a plurality of frequencies, the methodcomprising: (a) analyzing the multicarrier symbol to detect a peak inthe multicarrier symbol; (b) determining a first signal of the pluralityof signals that contributes to the peak; and (c) modifying the firstsignal by applying a peak reduction component to the first signal, thepeak reduction component including a transmission channel component suchthat by the PAR of the multicarrier symbol is reduced to compensate forthe transmission channel effects on the power of the symbol.
 4. A methodas defined in claim 3 , wherein said transmission channel effectsrepresent an impulse response of the transmission channel.
 5. A methodas defined in claim 3 , said transmission channel component includingtransmission filters, and said impulse response being the impulseresponse of said filters.
 6. A transmitter for use in a communicationsystem, the transmitter transmitting a signal where the transmittedsignal has a peak to average power ratio and is a function of aplurality of information symbols, each symbol being transmitted at eachone of a plurality of intervals of time, a selected information symbolof the plurality of information symbol including an informationcomponent and a peak reduction component and wherein the peak reductioncomponent is modified to compensate for transmitted filter responses inthe transmitter and wherein the modified peak reduction componentmodifies the information component and reduces the peak to average ratioof the transmitted signal.
 7. A transmitter for use in a multicarriercommunication system where a symbol transmitted by a transmitter haspeak to average power ratio as a function of a plurality of signals,each one of the plurality of signals being centered at one of pluralityof frequencies wherein a subset of the plurality of signals areconfigured to reduce the PAR before the symbol is transmitted along atransmission channel and where the subset of signals are furtherconfigured to include a response of the transmission channel.
 8. Atransmitter as defined in claim 7 , including: (a) an encoder forencoding a first set of data into a plurality of sets of data; (b) amodulator coupled to the encoder for receiving the plurality of sets ofdata and (c) modulating each set of data of the plurality of the sets ofdata to produce the plurality of signals which are combined; (c) a firstinverse Fourier transformer coupled to the modulator, the inverseFourier transformer operative to perform an inverse Fourier transform onthe combined plurality of signals producing a transformed signal; (d) afirst power reducer coupled to the inverse transformer, wherein thepower reducer is operative to analyze the transformed signal and todetect any peaks in the transformed signal, and if a peak is detected,the power reducer being operative to apply a kernel to the peak of thetransformed signal by adjusting the kernel, wherein the kernel is anapproximation of an impulse response generated from the subset of theplurality of signals such that the kernel is adjusted by scaling andtime shifting; and (e) a second power reducer coupled to receive aweighted transformed signal and a weighted kernel for analyzing theweighted transformed signal and for detecting any peaks therein if apeak is detected, the second power reducer being operative to apply theweighted kernel to the weighted transformed signal by applying scale andshift values to the weighted kernel such that said scale and shiftvalues are used by said first power reducer for respectively scaling andtime shifting said kernel, such that said weighting includes the effectsof said transmission channel.
 9. A transmitter as defined in claim 7 ,further including: (f) a cyclic prefix insertion module coupled to saidinverse Fourier transformer; (g) a filter for receiving an output fromsaid cyclic prefix insertion module; and (h) a power reducer coupled tothe output of said filter, wherein the power reducer is operative toanalyze the output from said cyclic prefix model to detect peaks in thesignal, and if a peak is detected, the power reducer is operative toapply a modified kernel to the peak of the signal by adjusting themodified kernel wherein the kernel is an approximation of an impulseresponse generated from the subset of the plurality of signals such thatthe kernel is adjusted by modifying the subset of plurality of signalsand wherein the kernel is further modified using the impulse response ofthe filter to produce the modified kernel whereby the effect of thefilter is included in the reduced PAR of the symbol.
 10. A transmitteras defined in claim 8 , wherein the transmitter is an XDSL transmitter.11. A transmitter for transmitting a Discrete Multi Tone (DMT) signalcomprising: (a) a kernel generator for generating a kernel signal forreducing peaks of said DMT signal; (b) a PAR reducer for modifying thephase and amplitude of said kernel signal and adding it to said DMTsignal; and (c) at least one filter for filtering said DMT signal;wherein said kernel generator is operative to reduce the peaks of saidDMT signal such that the PAR is reduced after said filter.